The paper introduces SINGER, a novel method for Bayesian inference of Ancestral Recombination Graphs (ARGs) from large genome samples. SINGER accelerates the sampling of ARGs from the posterior distribution by two orders of magnitude, enabling accurate inference and uncertainty quantification. The method is evaluated through extensive simulations, demonstrating enhanced accuracy and robustness to model misspecification compared to existing methods. SINGER is applied to African populations within the 1000 Genomes Project, revealing signals of local adaptation, archaic introgression, trans-species polymorphism, and balancing selection in HLA regions. The paper also discusses the limitations and potential improvements of SINGER, including the need for more efficient ARG exploration strategies and the ability to handle unphased data.The paper introduces SINGER, a novel method for Bayesian inference of Ancestral Recombination Graphs (ARGs) from large genome samples. SINGER accelerates the sampling of ARGs from the posterior distribution by two orders of magnitude, enabling accurate inference and uncertainty quantification. The method is evaluated through extensive simulations, demonstrating enhanced accuracy and robustness to model misspecification compared to existing methods. SINGER is applied to African populations within the 1000 Genomes Project, revealing signals of local adaptation, archaic introgression, trans-species polymorphism, and balancing selection in HLA regions. The paper also discusses the limitations and potential improvements of SINGER, including the need for more efficient ARG exploration strategies and the ability to handle unphased data.